Influence of hydrogen core force shielding on dislocation junctions in iron

The influence of hydrogen on dislocation junctions has been analyzed by incorporating a hydrogen-dependent core force into nodal-based discrete dislocation plasticity simulations. Hydrogen reduces the core energy of dislocations, which reduces the magnitude of the dislocation core force. We refer to this as hydrogen core force shielding, as it is analogous to hydrogen elastic shielding but occurs at much lower hydrogen concentrations. The dislocation core energy change due to hydrogen was calibrated at the atomic scale, accounting for the nonlinear interatomic interactions at the dislocation core, giving the model a sound physical basis. Hydrogen was found to strengthen binary junctions and promote the nucleation of dislocations from triple junctions. Simulations of microcantilever bend tests showed hydrogen core force shielding reduced the yield stress followed by increased strain hardening due to junction strengthening. These simulations demonstrate hydrogen effects at a small bulk hydrogen concentration, 10 appm, realistic for body-centered cubic iron, allowing micromechanical tests on hydrogen charged samples to be simulated.

Figure 1

The calibrated hydrogen core energy for $1/2\langle 111\rangle$ and $\langle 100\rangle$ dislocations. The hydrogen core energy is negative and so will reduce the total core energy and total core force. We refer to this as hydrogen core force shielding, as it is analogous to hydrogen elastic shielding [7].

Figure 2

Illustration of the binary junction geometry: (a) the initial configuration and (b) the junction formed after relaxation. The initial dislocations and the junction are of pure edge type.

Figure 3

Variation of junction length with hydrogen concentration calculated via the line tension (LT) model.

Figure 4

(a) Variation of junction length with hydrogen concentration calculated via DDD without considering hydrogen core force shielding and (b) with hydrogen core force shielding.

Figure 5

The effect of hydrogen on binary junction (a) length and (b) strength.

Figure 6

The nodal force partitioned into hydrogen, ${\mathit{F}}^{c,H}$ (blue arrows), and nonhydrogen parts ${\tilde{\mathit{F}}}_k+{\widehat{\mathit{F}}}_k+{\mathit{F}}^c$ (green arrows). (a) Formation (zipping) of a [001] junction. (b) Destruction (unzipping) of the junction. The end points of the junction are marked with red circles; note ${\mathit{F}}^{c,H}$ has been scaled $5\times$ for clarity.

Figure 7

A screw triple junction operating as a F-R source. (a) Initial triple junction before bow out; (b) Interaction between the $1/2\langle 111\rangle$ (black) dislocation loop and the $1/2\left[11\overline{1}\right]$ (green) arm on the left, forming a $\left[00\overline{1}\right]$ sessile dislocation (red): $1/2\left[11\overline{1}\right]\left(1\overline{1}0\right)+1/2\left[\overline{1}\overline{1}\overline{1}\right]\left(1\overline{1}0\right)\to \left[00\overline{1}\right]\left(1\overline{1}0\right)$; (c) $1/2\langle 111\rangle$ loop has bowed back, restoring the $1/2\left[11\overline{1}\right]$ arm, and the process then occurs on the right. (d) Moment just before the emission of a full loop, restoring the triple junction as in panel (a), and the process repeats.

Figure 8

Variation of (a) triple junction length and (b) strength with initial dislocation length, with and without hydrogen.

Figure 9

The nodal force partitioned into hydrogen core force, ${\mathit{F}}^{c,H}$ (blue arrows), and nonhydrogen parts ${\tilde{\mathit{F}}}_k+{\widehat{\mathit{F}}}_k$ (green arrows). (a) Formation of the triple junction. (b) Bow out of the junction. The ending points of the junction in panel (a) are marked with red circles; note ${\mathit{F}}^{c,H}$ has been scaled $20\times$ with respect to ${\tilde{\mathit{F}}}_k+{\widehat{\mathit{F}}}_k$ for clarity.

Figure 10

(a) The load-displacement curve; (b) the evolution of the total dislocation density.

Figure 11

(a) The evolution of binary dislocation junction density; (b) the evolution of multiple dislocation junction density.

Figure 12

Dislocation structure in the initial loading stage $U=-50$ nm: (a) without hydrogen and (b) with hydrogen. The dislocations belonging to the three initial slip systems are $1/2\left[\overline{1}11\right]\left(01\overline{1}\right)$ (black), $1/2\left[1\overline{1}1\right]\left(10\overline{1}\right)$ (blue), and $1/2\left[11\overline{1}\right]\left(1\overline{1}0\right)$ (green) with binary junctions (red) and multiple dislocation junctions (magenta).

Figure 13

Dislocation structure at $U=-90$ nm: (a) without hydrogen and (b) with hydrogen. With the same color coding as Fig. 12.

Figure 14

Variation of the (a) length and (b) strength of binary junctions with different $\langle 100\rangle$ binding energies. The three cases $+10\%$, $-20\%$, and $-40\%$ and the original case are shown. These figures correspond to Figs. 4 and 5, respectively.

Figure 15

(a) The load-displacement curves extracted from the microcantilever simulations; (b) the evolution of binary junction density during the loading of the microcantilevers. These figures correspond to Figs. 10 and 11, respectively.